Question

The functions f(x) = (x + 1)2 − 2 and g(x) = -(x − 2)2 + 1 have been rewritten using the completing-the-square method. Is the vertex for each function a minimum or a maximum? Explain your reasoning for each function.

Answer 1

Answer:

see explanation

Step-by-step explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

• If a > 0, then vertex is a minimum

• If a < 0, then the vertex is a maximum

for f(x) = (x + 1)² - 2 ← with a = 1 > 0

then vertex (- 1, - 2) is a minimum

for g(x) = - (x - 2)² + 1 ← with a = - 1 < 0

then vertex (2, 1) is a maximum